3.7 \(\int \sec ^2(x) \, dx\)

Optimal. Leaf size=2 \[ \tan (x) \]

[Out]

Tan[x]

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Rubi [A]  time = 0.00792822, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ \tan (x) \]

Antiderivative was successfully verified.

[In]  Int[Sec[x]^2,x]

[Out]

Tan[x]

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Rubi in Sympy [A]  time = 0.471343, size = 5, normalized size = 2.5 \[ \frac{\sin{\left (x \right )}}{\cos{\left (x \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(sec(x)**2,x)

[Out]

sin(x)/cos(x)

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Mathematica [A]  time = 0.00265266, size = 2, normalized size = 1. \[ \tan (x) \]

Antiderivative was successfully verified.

[In]  Integrate[Sec[x]^2,x]

[Out]

Tan[x]

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Maple [A]  time = 0.005, size = 3, normalized size = 1.5 \[ \tan \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(sec(x)^2,x)

[Out]

tan(x)

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Maxima [A]  time = 1.36381, size = 3, normalized size = 1.5 \[ \tan \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sec(x)^2,x, algorithm="maxima")

[Out]

tan(x)

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Fricas [A]  time = 0.206787, size = 9, normalized size = 4.5 \[ \frac{\sin \left (x\right )}{\cos \left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sec(x)^2,x, algorithm="fricas")

[Out]

sin(x)/cos(x)

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Sympy [A]  time = 0.044717, size = 5, normalized size = 2.5 \[ \frac{\sin{\left (x \right )}}{\cos{\left (x \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sec(x)**2,x)

[Out]

sin(x)/cos(x)

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GIAC/XCAS [A]  time = 0.208382, size = 3, normalized size = 1.5 \[ \tan \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sec(x)^2,x, algorithm="giac")

[Out]

tan(x)